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AUTHOR
TITLE
INSTITUTION
SPONS AGENCY
PUB DATE
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PUB TYPE
Rasmus sen 9 Bonnie
Pre-SPC Math for Foundry Workers. A Lesson Developed
for Robinson Foundry and Bodine-Robinson as Part of a
National Workplace Literacy Program.
Central Alabama Community Coll., Alexander City.
Office of Vocational and Adult Education (ED),
Washington, DC. National Workplace Literacy
Program.
Mar 93
81p.; For related workplace literacy basic skills
documents, see ED 352 463-464.
Guides - Classroom Use - Teaching Guides (For
Teacher) (052) — Tests/Evaluation Instruments (160)
EDRS PRICE
DESCRIPTORS
IDENTIFIERS
MF01/PC04 Plus Postage.
Addition; Adult Basic Education; Arithmetic; Decimal
Fractions ; ^'Foundries ; ^Individual ized Instruction;
Instructional Materials; Integrated Curriculum;
^'^Mathematics Instruction; Metal Industry; Metal
Working; ""^Pacing; '^Quality Control; Standards;
Subtraction; Units of Study
National Workplace Literacy Program; ^Statistical
Process Control; ^Workplace Literacy
ABSTRACT
Developed as part of a National Workplace Literacy
Program, this lesson focuses on terms and mathematical operations
associated with Statistical Process Control (SPC) in the foundry
industry. With appropriate assistance and preparatory work, workers
testing between grades 4 and 9 on the Test of Adult Basic Education
Locator should be able to use the lesson. The individualized lesson
is intended to supplement small-group SPC activities. It teaches
terms and mathematics used in quality control at Bodine-Robinson and
Robinson Foundry. Reading material is followed by questions that ask
about the instructional material. Some terms that are covered include
key characteristic, specification, aim, and control limits.
Mathematics areas include adding and subtracting SPC measurements,
adding and subtracting decimals, figuring averages, and figuring
ranges. A true-false quiz on the material is provided. (YLB)
Reproductions supplied by EDRS rre the best that can be made *
* from the original document. *
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PRE-SPC MATH FOR FOUNDRY WORKERS
A Lesson Developed for Robinson Foundry and Bodine-Robinson as
part of a National Workplace Literacy Program
March, 1993
This lesson was developed during a National Workplace
Literacy Project to augment small group teaching. The
lesson teaches math and reading skills needed by workers
in the metalcasting industry. Skills and understandings
focused on include these: adding, subtracting and dividing
decimal numbers; figuring averages and ranges;
understanding percentages; reading chemistry symbols;
using SPC terminology; using metalcasting terminology; and
using information presented in table form.
The learning package is structured to be used by
individual learners. They read, study charts, answer
questions about the information, and check whether their
answers are correct. Responses for both correct and
incorrect answers reinforce learning. A pre- and post-test
is included.
Bonnie Rasmussen
Curriculum Development Specialist
INTRODUCTION
PO Box 1235
Alexander City, AL 35010
205 329 8481
ERIC
2 BEST COPY fiEILSBlE
In this lesson on
Pre-SPC MATH
you will learn about the terms and math used in Quality Control
at Bodine-Robinson and Robinson Foundry.
As you read through the lesson, you will be asked questions about
what you are learning.
Finally, you will do a short quiz on the lesson.
ERLC
1
SPC charts keep track of key characteristics in the manufacturing
process. For instance, charts keep track of these things:
amount of zinc in the holding furnace when pouring Ford Manifolds
amount of moisture content in sand from suppliers
amount of silicon in a test button from CL 30a iron
A wrong amount of any key characteristic gives you a defect. For
example, too much silicon in CL 30a makes brittle iron.
The right amount for each key characteristic is figured out by
the lab.
Here are two specifications the lab has set for new sand in the
Bodine-Robinson process .
B-R NEW SAND
key characteristic specification
moisture content . 1% maximum
loss on ignition .22% maximum
moisture content: amount of water in the sand
loss on ignition: amount of material in the sand mixture that
is not sand (for instance, sticks that
ignite, or burn up, during testing)
3
BEST COPY AVAILABLE
ERIC
The lab's specification often sets a maximum for a key
characteristic. You can't have more than •!% of moisture in new
sand, for instance.
B-R New Sand
key characteristic specification
% moisture content .1 maximum
BEST COPY AVAILABLE
other times, the specification will be an exact number, or
aim point. You should try to get exactly 3.25% carbon in CL 30a
iron. 3.25% is the aim.
key characteristic
% carbon (CL 25 iron)
% carbon (CL 20 iron)
% carbon (CL 30a iron)
% carbon (CL 35 iron)
R-F CL 30a iron
Specification
Aim
3.49
3.90
3.25
3.15
BEST COPY AVAILABLE
since you can't hit the aim point exactly every time, upper
control limits (UCL) and lower control limits (LCL) are also set
by the lab. In other words, CL 30a iron is OK if you get between
3*20% and 3.30% of carbon. (You might notice that the aim point,
3.25%, is right in the middle of the UCL and LCL.)
RF CL 30a iron
Xey characteristic
Specification
Aim
Control Limits
% carbon (CL 25 iron)
% carbon (CL 20 iron)
% carbon (CL 30a iron)
% carbon (CL 35 iron)
3.49
3.90
3.25
3.15
3.44
3.80
3.20
3.00
3.54
4.80
3.30
3.10
SESf COPY mum
Let's look at the aim and control limits of CL 30a iron to see
what they mean. The measurements have to do with the amount of
carbon and other ingredients in the mix.
key characteristic Specification
Aim Control Limits
% carbon (CL 30a iron) 3.25 3.20-3.30
The aim point is 3.25% The best amount of carbon in CL 30a
iron is 3.25%
BEST COPY AVAILABLE
In the square below, 3,25% is darkened.
ii
The square has been divided into 100 equal small squares. Three
small squares along with a fourth of another square is equal to
3.25% That portion of the iron mix should be carbon.
Obviously, very small amounts of carbon make a big difference.
8
In the square below, 10.00% is darkened.
■
■
■
■
■
■
■
■
■
■
■
■
■
■
■
■
■
■
■
■
i
■
■
■
■
■
■
■
■
E
■
■
The square has been divided into 100 equal small squares. 10 of
the small squares is equal to 10.00%
9
In the square below, what percentage is darkened?
a
Of the 100 equal small squares, 1 1/2 squares or 1.5% has been
darkened.
10
ERIC
12
Most of the key characteristic specifications are for very small
amounts. Here are the aim point percentages, in color, for CL
30a iron:
Aim color
% carbon 3.25 bUie
% silicon 2.15 yellow
% manganese .55 pink
% chromium .08 green
% carbon
Aim
3.25
If the Quick Lab shows that the amount of carbon is 2.25%, you
need to know how far off you are from the aim point.
Subtract like this: 3.25
- 2.25
1.00
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Jc;^^ COPY AVAILABLE
14
You can add and subtra^-t SPC measurements, as long as you line up
the decimal points, like this:
3.5 6.4
+ 3^ - 3^
6.6 3.4
13
JL O
What is the answer to these problems?
3.5
+ 3.5
6.4
- .5
Add the two fives,
carry the one, and
add 3+3+1 to get 7.0
3.5
+ 3.5
7 . 0
Borrow one from the six,
subtract 5 from 14 to get
9. Then subtract 0 from
5 to get 5 .
6.4
- .5
5.9
14
ERIC
You need to be able to add and subtract decimals to use SPC
control charts.
The next few pages will review SPC words we've been using, and
give you practice in adding and subtracting decimal numbers.
Use the answer sheet for writing down your answers. DO NOT WRITE
IN THIS BOOK.
15
± i
What fits best in the blank below?
aO (UCL) Upper Control Limit
b*) key element
c/) random sample
A wrong amount of any gives you a defect. For
instance, too much silicon in CL 30a makes brittle iron.
Turn the page for the correct answer.
a* This is not the right answer.
The Upper Control Limit (UCL) shows how high a measurement can be
and still be OK. For instance, the UCL for carbon in CL 30a iron
is 3.30
b. This is the correct answer.
A wrong amount of any key element gives you a defect. For
instance, too much silicon in CL 30a makes brittle iron.
c. This is not the best answer.
A random sample is taken and put on the control chart. But the
sample is of a key element, such as silicon, carbon, and other
elements.
17
What fits best in the blank below?
a*) (UCL) Upper Control Limit
bO key element
c.) random sample
SPC charts keep track of each
manufacturing process •
Turn the page for the correct answer.
18
a. This is not the right answer.
The Upper Control Limit (UCL) shows how high a measurement can be
and still be OK. For instance, the UCL for carbon in CL 30a iron
is 3.30
b* This is the correct answer.
SPC charts keep track of each key element in the manufacturing
process .
c. This is not the best answer.
An aim point is the measurement you want to achieve. But what
you are measuring is the amount of a key element.
19
21
What fits best in the blank below?
a,) specification
h.) estimation
c.) sample
The lab's often sets a maximum for a key
characteristic. You can't have more than •!% of moisture in new
sand, for instance.
Turn the page for the correct answer.
ERLC
20
22
a. This is the correct answer.
The lab's specification often ssts a maximum for a key
characteristic. You can't have more than .1% of moisture in new
sand, for instance.
b. This is not the right answer.
An estimation is a guess or an approximation. A specification,
on the other hand, is the number set by the lab as the goal.
c. This is not the right answer.
A sample is a part of the work that is measured and put on the
control chart. But the specification is the number set by the
lab as the goal.
Which of the following words fits best in the blank below?
a . ) specification
b. ) estimation
c. ) sample
Other times, the will be an exact number, or
aim point. You should try to get exactly 3.25% carbon in CL 30a
iron.
Turn the page for the correct answer.
a. This is the correct answer.
Other times, the specification will be an exact number, or aim
point. You should try to get exactly 3.25% carbon in CL 30a
iron.
h. This is not the right answer.
An estimation is a guess or an approximation. A specification,
on the other hand, is the number set by the lab.
c. This is not the right answer.
A sample is a part of the work that is measured ana put on the
control chart. But the specification is the number set by the
lab as the goal.
what fits best in the blank below?
a. ) control chart
b. ) key element
c. ) random sample
The right amount for each
lab.
is figured out by the
Turn the page for the correct answer <
24
ERLC
a. This is not the best answer •
A control chart is a graph which shows you how well your job is
running.
b. This is the correct answer.
The right amount for each key element is figured out by the lab.
c. This is not the best answer.
A random sample is taken and put on the control chart. But the
sample is of a key element, such as silicon, carbon, and other
elements .
ERLC
25
What fits best in the blank below?
a. ) statistical process co trol (SPC) and non-statistical
process control (N-SPC)
b. ) lost foam process (EPS) and Evaporative Polystyrene System
(EPS)
c. ) upper control limits (UCL) and lower control limits (LCL)
You might notice that the aim point, 3.25%, is right in the
middle of the and
Turn the page for the correct answer.
a. This is not the right answer •
Statistical process control (SPC) is a way of using number facts
to keep track of quality.
The upper and lower control limits, on the other hand, are found
on SPC charts. If sample measurements fall within the upper and
lower control limits, things are going OK.
b. This is not the right answer.
The lost foam process is another name for the Evaporative
Polystyrene System, or EPS.
The upper and lower control limits, on the other hand, are found
on SPC charts. If sample measurements fall within the upper and
lower control limits, things are going OK.
c. This is the correct answer.
You might notice that the aim point, 3.25%, is right in the
middle of the upper control limits UCL) and lower control limits
(LCD .
What percentage of the large square is darkened?
a. 50 of the hundred small squares, or 50%
b. 3 of the hundred small squares, or 3.0%
c. 1 and-a-half of the hundred small squares, or 1.5%
Turn the page for the correct answer.
ERIC
m\ mn available
28
a. This is the correct answer.
Fifty of the hundred small squares, or 50% are darkened.
b. This is not the right answer.
Count the squares to get the right aiiswer: 50/100
c. This is not the right answer.
Count the squares to get the right answer: 50/100
What percentage of the large square is darkened?
a. Fifty of the hundred small squares, or 50%
b. Three of the hundred small squares, or 3.0%
c. One and-a-half of the hundred small squares, or 1.5%
J' .* * ft
Turn the page for the correct answer.
30
ERIC
a. This is not the right answer.
Count the squares to get the right answer: 3/100
b. This is the correct answer.
Three of the hundred small squares, or 3.0% are darkened.
c. This is not the right answer.
Count the squares to gei: the right answer: 3/100
31
What percentage of the large square is darkened?
a. Fifty of the hundred small squares, or 50%
b. Three of the hundred small squares, or 3,0%
c. One and-a-half of the hundred small squares, or 1,5%
Turn the page for the correct answer.
ERIC
32
a. This is not the right answer.
Count the squares to get the right a*-swer: 1 1/2/100
b. This is not the right answer.
Count the squares to get the right answer: 1 1/2/100
c. This is the correct answer.
One-and-a-half of the hundred small squares, or 1.50% are
darkened .
33
4^
What percentage of the large square is darkened?
a. ) Ten of the hundred small squares, or 10%
b. ) Three of the hundred small squares, or 3.0%
c. ) One-and-a-half of the hundred small squares, or 1.5%
1
1
Turn the page for the correct answer.
34
ERIC
a. This is the correct answer.
Ten of the hundred small squares, or 10% are darkened.
This is not the right answer.
Count the squares to get the right answer: 10/100
c. This is not the right answer.
Count the squares to get the right answer: 10/100
ERLC
35
O 4
What is the correct answer?
1.25%
+ 1.01%
a. ) 2.80%
b. ) 2.26%
C.) 22.6%
Turn the page for the correct answer.
ERIC
36
a. This is not the right answer.
b. This is the correct answer.
1.25%
+1.01%
2.26%
o. This is not the right answer.
37
ERIC
9^ G;}
What is the correct answer?
1.90
+ 1.20
a. ) 2.11
b. ) 3.11
c. ) 3.10
Turn the page for the correct answer.
ERIC
38
40
a. This is not the right answer.
b. This is the correct answer.
1.90
+ 1.20
3.11
c. This is not the right answer.
39
What is the correct answer?
3.25
- 3.00
a. ) .25
b. ) 6.25
c. ) 25.00
Turn the page for the correct answer.
ERIC
40
This is the correct answer.
3.25
3.00
.25
This is not the right answer.
This is not the right answer.
What is the correct answer?
3 .50
- 2.19
a. ) 1.31
b. ) 1.41
c. ) 0.131
Turn the page for the correct answer.
ERIC
42
-^4
This is the correct answer.
3.50
2.19
1.31
This is not the right answer
This is not the right answer
You have finished the review questions on terms and math for the
first part of the lesson. Now you'll learn about more terms and
math used in Quality Control at Bodine-Robinson and Robinson
Foundry .
Each time an SPC measurement is taken for a Key Characteristic,
you get some idea of how close you are to the lab's
specif ication* If you write down several of the measurements, you
can average them.
ERIC
44
- HO
Here's how you figure an average:
The amount of silicon measures at 7.09, then at 7.04, and finally
at 6.93.
Add up the measurements: 7.19
7.24
+ 6.93
21.36
Divide by 3, since there
are three measurements 7 . 12
you added together : 3/21.36
21
0 3
3
06
_6
0
The average amount of silicon that shift was 7.12
45
ERIC
An average, then, evens out the high and low measurements, like
this:
Two are six feet tall,
two are five feet tall.
6
6
H
3
I
"7
All four are now five-and-a-half feet tall.
5
3
l
/
46
ERIC
Here's another example of how to figure an average. (By the way,
the silicon itieasureitients we are averaging are those taken in the
holding furnace when pouring Ford Manifolds. The aim point is
7.25.)
7.00
7.34
+ 7.38
21.72
7.24
3/21.72
47
Why, in this example do we divide by
7 .00
7.40
6.93
+ 7.25
28.58
7.15
4/28.58
48
If you have four measurements, you have to divide by four.
(You always divide by the number of measurements.)
The next few pages will give you practice in adding and
subtracting decimal numbers.
Use thfe answer sheet f.r writing down your answers. DO NOT WRITE
IN THIS BOOK.
49
51
On SPC charts you will see an X. That means average, and is
pronounced ' X-bar ' .
What is the correct answer?
4
4
+7
15
5
3/15
a. X = 15
b. X = 5
C. X = 3
Turn the page for the correct answer.
50
a. This is not the right answer.
Fifteen is the sum of the sample measuremonts .
b. This is the correct answer.
4
4
±2
15
_5
3/15
Average (X) = sum of samples
niunber of samples
e. This is not the right answer.
Three is the number of sample measurements.
51
ERIC
What is the correct answer?
1
4
+7
3/
a.
X =
12
b.
X =
5
c.
X =
4
Turn the page for the correct an. wer.
ERIC
52
This is not the correct answer
This is not the correct answer
This is the correct answer.
1
4
±z
12
4
3/12
Average (X) = sim of samples
niimber of samples
What is the correct answer?
3.25
3.23
/
a.
X =
3
.24
b.
X =
4
.24
c.
X =
6
.46
Turn the page for the correct answer.
54
5d
a. This is the correct answer.
3.25
3.23
6.48
3 .24
2/6.48
Average (X) = sxim of samples
number of samples
b. This is not the correct answer
c. This is not the correct answer
55
What is the correct answer?
7.21
7.44
+1 .21
I
a. X = 21.92
b. X = 10.96
C. X = 7.31
Turn the page for the correct answer.
ERIC
56
58
a.
This is not the correct answer.
b. This is not the correct answer.
c. This is the correct answer.
7.21
7.44
+7.27
21.92
7.31
3/21.92
Average (X) = stun of samples
number of samples
ERIC
57
Another important SPC term is ra
the range of the second group of
on the left?
Problem 1: What is the
range of the three
measurements?
ga, or R. Can you figure out
numbers by studying the example
Problem 2: What is the
range of the three
measurements?
Measurements
7,21
7,44
7,27
Measurements
7,01
7,04
6.93
7.44
-7.21
.23
R
23
R
58
CO
Measurements
Arithmetic to figure R
7.01
7.04
6.93
7.04
- 6.93
.11
= .11
Just subtract the smallest measurement from the biggest
measurement .
The next few pages will give you practice in figuring ranges.
Use the answer sheet for writing down your answers. DO NOT WRITE
IN THIS BOOK.
59
61
What is R?
7.74
7.28
7.20
a.
R =
.46
b.
R =
.54
c.
R =
7.41
Turn the page for the correct answer.
60
ERIC
a. This is not the right answer.
b. This is the correct answer.
Correct arithmetic
7.74
- 7.20
.54 = R
Sample measureiaents
7.74
7.28
7.20
Range (R) = Largest measurement minus smallest measurement
c. This is not the right answer.
What is R?
7.44
7.46
7.48
a.
R =
.02
b.
R =
.04
c.
R =
.06
Turn the page for the correct answer.
62
a* This is not the right answer.
b* This is the correct answer.
Sample measurements Correct arithmetic
7.44 7.48
7.46 - 7.44
7.48 .04 = R
Range (R) = Largest measurement minus smallest measurement
c. This is not the right answer.
63
What is R?
7.44
7.44
7.41
a. R = 7.43
b. R = .03
C. R = 1.29
Turn the page for the correct answer.
ERIC
64
a. This is not the right answer.
b.
This is the correct answer.
Sample measurements
7 .44
7.44
7 .41
Correct arithmetic
7 .44
- 7.41
.03 = R
Range (R) = Largest measurement minus smallest measurement
c. This is not the right answer.
You have finished the review questions on terms and math for the
lesson. The next few pages explain further how the average (X)
and Range (R) give useful quality control information.
ERIC
65
C7
Below, the average column on the right shows us how close we are
to the aim point after smoothing out the highs and lows of
individual measurements.
Another way of looking at it is this: if the first three furnaces
(measuring 7.01, 6.82, 7.22) could be mixed together, the whole
big batch would measure 7.02.
(Remember, this example is of the percentage of silicon in the
holding furnace when pouring Ford Manifolds, and the aim point is
Measurements
Average (X)
7.01, 6.82, 7.22
7.00, 7.08, 6.93
7.21, 7.44, 7.27
7.02
7.00
7.31
7.25.)
What would you expect the missing numbers to be, approximately
Measurements
Average (X)
7.01, 6.82, 7.22
7.02
7.00, 7.08, 6.93
7 . 00
7.21, 7.44, 7.27
7 .31
7.04
, f
67
Did you expect one of the missing numbers to be as high as 12.05,
or as low as 2.00?
Measurements Average (X) Range (R)
7.01, 6.84, 7.22 7.02 .38
7.00, 7.08, 6.95 7.02 .13
7.02, 2.00, 12.05 7.02 10.05
Of course, a measurement of either 2.00 or 12.05 (for silicon in
the holding furnace when pouring Ford manifolds) would be very
unusual .
ERIC
68
7U
The point is, though, the average (X) smooths out the
differences, while the range (R) shows us how far apart the
measurements are.
Measurements Average (X) Range (R)
7.01, 6.84, 7.22 7.02 .38
7.00, 7.08, 6.95 7.02 .13
7.02, 2.00, 12.05 7.02 10.05
69
ERIC
without the range, you can't predict accurately. Look at the
ways that 3 numbers can average the same but have different
ranges.
Measurements
Average (X)
Range
7.01, 6.84, 7.22
7.02
.38
7.00, 7.08, 6.95
7.02
.13
7.02, 2.00, 12.05
7.02
10.05
70
In this lesson you have learned about the terms and
math used in SPC.
Next you will do a short quiz.
Use the answer sheet for writing down your answers. DO NOT WRITE
IN THIS BOOK.
71
o 73
ERIC
Quis
Answer true or false for each question.
1. The lab's specification for a key element may be a maximum or
a minimum, but never an aim point.
a . ) true
b. ) false
2. The Control Limits for CL 30a iron are 3.20-3.30. That
means that a measurement of 3.24 is within the limits.
a . ) true
b. ) false
3. A large square is divided into 100 equal smaller squares.
Three and a half small squares are equal to 3.5% of the large
square .
a . ) true
b. ) false
4. 3.25
+ 3.25
6.50
a . ) true
b. ) false
5. 7.21
- 7.09
.13
6. X on an SPC chart means the average, or mean.
a . ) true
b. ) false
7. To figure an average (X), add up the items and divide by the
number of items added.
a . ) true
bO false
8. To figure a range, add the top two numbers*
a • ) true
b*) false
9. This average is figured correctly.
measurements arithmetic
7.02, 6.82, 7.22 7. 0 27 . 02
6.82
+ 7.22
21.06
3/21.06
a. )
b. )
true
false
10.
This range is figured correctly.
measurements
7.01, 6.32,
arithmetic
7.22
7.22
" 6.82
.40
a . ) true
b. ) false
Turn the page for the correct answers.
73
75
Answers to Quis
Answer true or false for cuicli question*
1. The lab's specification for a key element may be a maximum or
a minimum, but never an aim point.
false
2. The Control Limits for CL 3 0a iron are 3.20--3.30. That
means that a measurement of 3.24 is within the limits.
true
3. A large square is divided into 100 equal smaller squares.
Three and a half small squares are equal to 3.5% of the large
square.
true .
4. 3.25
4- 3,25
6.50
true
5. 7.21
- 7.09
.13
false
6. X on an SPC chart means the average, or mean,
true
7. To figure an average (X), add up the items and divide by the
number of items added.
true
8. To figure a range, add the top two numbers,
false
9. This average is figured correctly.
measurements arithmetic
7.02, 6.82, 7.22 7.0 27.02
6.82 3/21.06
21.06
+7.22
true
10. This range is figured correctly.
measurements arithmetic
7.01, 6.82, 7.22 7.22
- 6.82
.40
true
75
ERIC
ANSWER SHEET
For each question, circle your answer, then check (on the next
page in the lesson book) whether it is right.
page 16
a. )
b. )
c. )
Page 18
a. )
b. )
c. )
Page 20
a. )
b. )
c. )
Page 22
a. )
b. )
c. )
page 24
a. )
b. )
c. )
page 2 6
a. )
b. )
c. )
Page 28
a. )
b. )
c. )
1 o
ERIC
Page '30
a. )
b. )
c. )
Page 32
a. )
b. )
c. )
Page 34
a. )
b. )
c. )
page 36
a. )
b. )
c. )
Page 38
a. )
b. )
c. )
Page 40
a. )
b. )
c. )
Page 42
a. )
b. )
c. )
Page SO
a. )
b. )
c. )
Page 52
a. )
b. )
c. )
Page 54
a. )
b. )
c. )
Page 56
a. )
b. )
c. )
Page 60
a. )
b. )
c. )
Page 62
a. )
b. )
c. )
Page 64
a. )
b. )
c. )
Quiz
1.
a. ) true
b. ) false
2.
a • ) true
b.) false
3.
a . ) true
b. ) false
4.
a • ) true
b.) false
5.
a • ) true
b.) false
6.
a. ) true
b. ) false
7.
a . ) true
b. ) false
8.
a • ) true
b.) false
9.
a. ) true
b. ) false
10.
a. ) true
b. ) false
81
ERIC